"Light and ghosts have nothing to do with each other. A spirit can exist whether there is light or not. Inside, or outside of them!" Maybe he's wrong. Then he's just arguing to argue.

It's not that he doesn't like being called a nerd, but it's the idea this guy doesn't want to improve his magic, which would be really really helpful. The number of people Gokudera has not been able to help, that he's seen suffer... To take something like healing magic and think so little of it is offensive.

"I don't care what you think about light magic." Gokudera says, stubborn and not sitting back down. This guy hasn't proved that he's any kind of Demon King, and Gokudera thinks little of him now with his opinions on healing magic voiced. If they could trade magic, he would readily do so.